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Pair of Linear Equations in Two Variables
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28/05/2021 10:50 am
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Solve the following pairs of equations by reducing them to a pair of linear equations:
10/(x+y) + 2/(x-y) = 4
15/(x+y) – 5/(x-y) = -2
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28/05/2021 10:51 am
Substituting 1/x+y = m and 1/x-y = n in the given equations, we get,
10m + 2n = 4
=> 10m + 2n – 4 = 0 ………………..…..(i)
15m – 5n = -2
=> 15m – 5n + 2 = 0 ……………………..(ii)
Using cross-multiplication method, we get,
m/(4-20) = n/(-60-(20)) = 1/(-50 -30)
m/-16 = n/-80 = 1/-80
m/-16 = 1/-80 and n/-80 = 1/-80
m = 1/5 and n = 1
m = 1/(x+y) = 1/5
x+y = 5 ……………………(iii)
n = 1/(x-y) = 1
x - y = 1 …………………(iv)
Adding equation (iii) and (iv), we get
2x = 6 => x = 3 …….(v)
Putting the value of x = 3 in equation (3), we get
y = 2
Hence, x = 3 and y = 2